A wooden beam 4m long weighs 84kg. Determine the mass of a beam of 50cm long

To determine the mass of a 50 cm long wooden beam, given that a 4-meter (400 cm) beam weighs 84 kg, we first need to find the weight per meter (or per centimeter) of the beam. 

### Step-by-step Calculation:

1. **Find the weight per meter of the beam:**

   A 4-meter beam weighs 84 kg. The weight per meter (\(W_{\text{per meter}}\)) is:

   \[
   W_{\text{per meter}} = \frac{\text{Total weight}}{\text{Total length}} = \frac{84 \, \text{kg}}{4 \, \text{m}} = 21 \, \text{kg/m}
   \]

2. **Convert the length from meters to centimeters:**

   Since we want the weight of a 50 cm beam, convert the length from meters to centimeters:

   \[
   1 \, \text{m} = 100 \, \text{cm} \quad \Rightarrow \quad 0.5 \, \text{m} = 50 \, \text{cm}
   \]

3. **Calculate the weight of a 50 cm beam:**

   Since 50 cm is half a meter (0.5 m), the weight (\(W_{50 \, \text{cm}}\)) of the 50 cm beam is:

   \[
   W_{50 \, \text{cm}} = W_{\text{per meter}} \times 0.5 \, \text{m} = 21 \, \text{kg/m} \times 0.5 \, \text{m} = 10.5 \, \text{kg}
   \]

Thus, the mass of a 50 cm long beam is **10.5 kg**.

Would you like further details or have any questions?

Here are 5 related questions that expand on this topic:

1. What would be the mass of a 1.5-meter-long beam made from the same material?
2. If the beam's weight density remains constant, how much would a 2-meter-long beam weigh?
3. How would the mass change if the beam were made of a material that is 1.5 times denser?
4. How can you calculate the volume of the beam if its cross-sectional area is known?
5. What is the weight per centimeter of the beam?

**Tip:** When converting units, always ensure that you adjust both the numerator and the denominator to maintain consistency in calculations.

Learn how to calculate the mass of a 50 cm long wooden beam from a 4-meter beam weighing 84 kg. Step-by-step calculation provided with formulas for unit conversion and weight calculation.

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